NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Q.1 Solve
(a)$\frac{2}{3}+\frac{1}{7}$
(b)$\frac{3}{10}+\frac{7}{15}$
(c) $\frac{4}{9}+\frac{2}{7}$
(d) $\frac{5}{7}+\frac{1}{3}$
(e) $\frac{2}{5}+\frac{1}{6}$
(f) $\frac{4}{5}+\frac{2}{3}$
(g) $\frac{3}{4}?\frac{1}{3}$
(h) $\frac{5}{6}?\frac{1}{3}$
(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
(j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$
(k) $1\frac{1}{3}+3\frac{2}{3}$
(l) $4\frac{2}{3}+3\frac{1}{4}$
(m) $\frac{16}{5}?\frac{7}{5}$
(n) $\frac{4}{3}?\frac{1}{2}$

Answer :

(a)$\frac{2}{3}+\frac{1}{7}$
LCM of 7 and 3 = 21
$\frac{2\times 7}{3\times 7}+\frac{1\times 3}{7\times 3}$
= $\frac{14}{21}+\frac{3}{21}$
= $\frac{17}{21}$
(b)$\frac{3}{10}+\frac{7}{15}$
LCM of 10 and 15 = 30
$\frac{3\times 3}{10\times 3}+\frac{7\times 2}{15\times 2}$
= $\frac{9}{30}+\frac{14}{30}$
= $\frac{23}{30}$
(c) $\frac{4}{9}+\frac{2}{7}$
LCM of 9 and 7 = 63
$\frac{4\times 7}{9\times 7}+\frac{2\times 9}{7\times 9}$
= $\frac{28}{63}+\frac{18}{63}$
= $\frac{46}{63}$
(d) $\frac{5}{7}+\frac{1}{3}$
LCM of 7 and 3 = 21
$\frac{5\times 3}{7\times 3}+\frac{1\times 7}{3\times 7}$
= $\frac{15}{21}+\frac{7}{21}$
= $\frac{22}{21}$
(e) $\frac{2}{5}+\frac{1}{6}$
LCM of 5 and 6 = 30
$\frac{2\times 6}{5\times 6}+\frac{1\times 5}{6\times 5}$
= $\frac{12}{30}+\frac{5}{30}$
= $\frac{17}{30}$
(f) $\frac{4}{5}+\frac{2}{3}$
LCM of 5 and 3 = 15
$\frac{4\times 3}{5\times 3}+\frac{2\times 5}{3\times 5}$
= $\frac{12}{15}+\frac{10}{15}$
= $\frac{22}{15}$
(g) $\frac{3}{4}?\frac{1}{3}$
LCM of 4 and 3 = 12
$\frac{3\times 3}{4\times 3}?\frac{1\times 4}{3\times 4}$
= $\frac{9}{12}?\frac{4}{12}$
= $\frac{5}{12}$
(h) $\frac{5}{6}?\frac{1}{3}$
LCM of 6 and 3 = 6
$\frac{5}{6}?\frac{1\times 2}{3\times 2}$
= $\frac{5}{6}?\frac{2}{6}$
= $\frac{3}{6}$ = $\frac{1}{2}$
(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
LCM of 3, 4 and 2 = 12
$\frac{2\times 4}{3\times 4}+\frac{3\times 3}{4\times 3}+\frac{1\times 6}{2\times 6}$
$\frac{8}{12}+\frac{9}{12}+\frac{6}{12}$
$\frac{23}{12}$
(j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$
LCM of 2, 3 and 6 = 6
$\frac{1\times 3}{2\times 3}+\frac{1\times 2}{3\times 2}+\frac{1}{6}$
$\frac{3}{6}+\frac{2}{6}+\frac{1}{6}$
$\frac{6}{6}$ = 1
(k) $1\frac{1}{3}+3\frac{2}{3}$
= $\frac{4}{3}+\frac{11}{3}$
= $\frac{15}{3}$ = 5
(l) $4\frac{2}{3}+3\frac{1}{4}$
= $\frac{14}{3}+\frac{13}{4}$
LCM of 3 and 4 = 12
$\frac{14\times 4}{3\times 4}+\frac{13\times 3}{4\times 3}$
= $\frac{56}{12}+\frac{39}{12}$
= $\frac{95}{12}$ \)
(m) $\frac{16}{5}?\frac{7}{5}$
$\frac{9}{5}$ = $1\frac{4}{5}$
(n) $\frac{4}{3}?\frac{1}{2}$
LCM of 3 and 2 = 6
$\frac{4\times 2}{3\times 2}?\frac{1\times 3}{2\times 3}$
= $\frac{8}{6}?\frac{3}{6}$
= $\frac{5}{6}$ \)

Q.2 Sarita bought $\frac{2}{5}$ metre of ribbon and Lalita $\frac{3}{4}$ metre of ribbon. What is the total length of the ribbon they bought?

Answer :

Length of ribbon bought by Sarita = $\frac{2}{5}$ metre
Length of ribbon bought by Lalita = $\frac{3}{4}$ metre
$?$ Length of ribbon bought by Sarita and Lalita $\frac{2}{5}+\frac{3}{4}$
LCM of 5 and 4 = 20
$\frac{2\times 4}{5\times 4}+\frac{3\times 5}{4\times 5}$
= $\frac{8}{20}+\frac{15}{20}$
= $\frac{23}{20}$ = $1\frac{3}{20}$ meter

Q.3 Naina was given $1\frac{1}{2}$ piece of cake and Najma was given $1\frac{1}{3}$ piece of cake. Find the total amount of cake was given to both of them.

Answer :

Fraction of cake Naina got = $1\frac{1}{2}$ = $\frac{3}{2}$
Fraction of cake Najma got = $1\frac{1}{3}$= $\frac{4}{3}$
Total amount of cake given to both of them =
$\frac{3}{2}+\frac{4}{3}$
LCM of 2 and 3 = 6
$\frac{3\times 3}{2\times 3}+\frac{4\times 2}{3\times 2}$
= $\frac{9}{6}+\frac{8}{6}$
= $\frac{17}{6}$ = $2\frac{5}{6}$

Q. 4. Fill in the boxes:
(a) $??\frac{5}{8}=\frac{1}{4}$
(b) $??\frac{1}{5}=\frac{1}{2}$
(c) $\frac{1}{2}??=\frac{1}{6}$

Answer :

(a) $??\frac{5}{8}=\frac{1}{4}$
Or, $?=\frac{1}{4}+\frac{5}{8}$
= $\frac{1\times 2}{4\times 2}+\frac{5}{8}$
= $\frac{2}{8}+\frac{5}{8}$ = $\frac{7}{8}(b)\text{(}??\frac{1}{5}=\frac{1}{2}$
Or, $?=\frac{1}{2}+\frac{1}{5}$
= $\frac{1\times 5}{2\times 5}+\frac{1\times 2}{5\times 2}$
= $\frac{5}{10}+\frac{2}{10}$ = $\frac{7}{10}$
(C) $\frac{1}{2}??=\frac{1}{6}$
Or, $\frac{1}{2}?\frac{1}{6}=?$
Or, $?=\frac{1\times 3}{2\times 3}?\frac{1}{6}$
Or, $?=\frac{3}{6}?\frac{1}{6}$
Or, $?=\frac{2}{6}$ = $\frac{1}{3}$

Q.5 Complete the addition-subtraction box.

Answer :

Q6 A piece of wire $\frac{7}{8}$ metre long broke into two pieces. One piece was $\frac{1}{4}$ metre long. How long is the other piece?

Answer :

Total length of wire = $\frac{7}{8}$ metre
Length of one piece of wire = $\frac{1}{4}$metre
Length of other piece of wire = Length of the original wire and this one piece of wire
= $\frac{7}{8}?\frac{1}{4}$
= $\frac{7}{8}?\frac{1\times 2}{4\times 2}$
= $\frac{7}{8}?\frac{2}{8}$
= $\frac{5}{8}$

Q.7 Nandini’s house is $\frac{9}{10}$ km from her school. She walked some distance and then took a bus for $\frac{1}{2}$ km to reach the school. How far did she walk?

Answer :

Distance of the school from house = $\frac{9}{10}$ km
Distance she travelled by bus = $\frac{1}{2}$ km
Distance walked by Nandini = Total distance of the school – Distance she travelled by bus
= $\frac{9}{10}?\frac{1}{2}$
= $\frac{9}{10}?\frac{1\times 5}{2\times 5}$
= $\frac{9}{10}?\frac{5}{10}$
= $\frac{4}{10}$ = $\frac{2}{5}$ km

Q.8 Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is $\frac{5}{6}$ th full and Samuel’s shelf is $\frac{2}{5}$ th full. Whose bookshelf is more full? By what fraction?

Answer :

Fraction of Asha’s bookshelf = $\frac{5}{6}$
Fraction of Samuel’s bookshelf = $\frac{2}{5}$
$\frac{5}{6}$ and $\frac{2}{5}$
By cross multiplication
5×5 and 6×2
25 > 12
$\frac{5}{6}$ > $\frac{2}{5}$
$?$ Asha’s bookshelf is more full than Samuel’s bookshelf
Difference = $\frac{5}{6}$ - $\frac{2}{5}$
= $\frac{5\times 5}{6\times 5}$ - $\frac{2\times 6}{5\times 6}$
= $\frac{25}{30}$ - $\frac{12}{30}$
= $\frac{13}{30}$

Q.9 Jaidev takes$2\frac{1}{5}$ minutes to walk across the school ground. Rahul takes$\frac{7}{4}$ minutes to do the same. Who takes less time and by what fraction?

Answer :

Time taken by Jaidev to walk across the school ground =$2\frac{1}{5}$ = $\frac{11}{5}$ minutes
Time taken by Rahul to walk across the school ground = $\frac{7}{4}$ minutes
$\frac{11}{5}$ and $\frac{7}{4}$
By cross multiplication
11×4 and 5×7
44 > 35
$\frac{11}{5}$ > $\frac{7}{4}$
$?$ Rahul takes less time than Jaidev to walk across the school ground
Difference = $\frac{11}{5}$ - $\frac{7}{4}$
= $\frac{11\times 4}{5\times 4}$ - $\frac{7\times 5}{4\times 5}$
= $\frac{44}{20}$ - $\frac{35}{20}$
= $\frac{9}{20}$

Q.1 Write the fraction representing the shaded portion.

Answer :

(i) Number of parts = 4
Shaded portion = 2
$?$ Fraction = $\frac{2}{4}$
(ii) Number of parts = 9
Shaded portion = 8
$?$ Fraction = $\frac{8}{9}$
(iii) Number of parts = 8
Shaded portion = 4
$?$ Fraction = $\frac{4}{8}$
(iv) Number of parts = 4
Shaded portion = 1
$?$ Fraction = $\frac{1}{4}$
(v) Number of parts = 7
Shaded portion = 3
$?$ Fraction = $\frac{3}{7}$
(vi) Number of parts = 12
Shaded portion = 3
$?$ Fraction = $\frac{3}{12}$
(vii) Number of parts = 10
Shaded portion = 10
$?$ Fraction = $\frac{10}{10}$
(viii) Number of parts = 9
Shaded portion = 4
$?$ Fraction = $\frac{4}{9}$
(ix) Number of parts = 8
Shaded portion = 4
$?$ Fraction = $\frac{4}{8}$
(x) Number of parts = 2
Shaded portion = 1
$?$ Fraction = $\frac{1}{2}$

Q.2 Colour the part according to the given fraction.

Answer :

Q.3 Identify the error, if any.

Answer :

(i) The parts are not equal
Hence, this is not $\frac{1}{2}$
(ii) the parts are not equal
Hence, Shaded portion is not $\frac{1}{4}$
(iii) the parts are not equal
Hence, Shaded portion is not $\frac{3}{4}$

Q.4 What fraction of a day is 8 hours?

Answer :

Since, a day has 24 hours and we have 8 hours
$?$ Required fraction = $\frac{8}{24}$

Q.5 What fraction of an hour is 40 minutes?

Answer :

Since 1 hours = 60 minutes
$?$ Fraction of 40 minutes = $\frac{40}{60}$

Q.6 Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?

Answer :

(a) Arya has divided the sandwich into 3 equal parts. So each person will get one part.
(b) Each boy receive $\frac{1}{3}$

Q.7 Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Answer :

Total number of dresses to be dyed = 30
Number of dresses finished = 20
$?$ Required fraction = $\frac{20}{30}=\frac{2}{3}$

Q.8 Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Answer :

Natural numbers between 2 and 12 are;
2,3,4, 5, 6, 7, 8, 9, 10,11, 12
No. of given natural numbers = 11
No. of prime numbers = 5
Hence, fraction = $\frac{5}{11}$

Q.9 Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Answer :

Natural numbers from 102 to 113 are;
102,103,104,105,106, 107,108, 109,110, 111, 112,113
Total number of given natural numbers = 12
Prime numbers are 103, 107, 109, 113 Number of prime numbers = 4
Hence, fraction = $\frac{4}{12}$ = $\frac{1}{3}$

Q.10 What fraction of these circles have X’s in them?

Answer :

Total number’of circles = 8
Number of circles having X’s in them = 4
Required fraction = $\frac{4}{8}=\frac{1}{2}$

Q.11 Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Answer :

Number of CDs bought by her from the market = 3
Number of CDs received as gifts = 5
Therefore Total number of CDs = 3 + 5 = 8
Therefore Fraction of CDs (bought) = $\frac{3}{8}$
and the fraction of CDs (gifted) = $\frac{5}{8}$

Q.1 Draw number lines and locate the points on them:
(a)$\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$
(b) $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$
(c) $\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}$

Answer :

Q.2 Express the following as mixed fractions:
(a)$\frac{20}{3}$
(b) $\frac{11}{5}$
(c) $\frac{17}{7}$
(d) $\frac{28}{5}$
(e) $\frac{19}{6}$
(f) $\frac{35}{9}$

Answer :

(a)$\frac{20}{3}$ = $6\frac{2}{3}$
(b) $\frac{11}{5}$ = $2\frac{1}{5}$
(c) $\frac{17}{7}$ = $2\frac{3}{7}$
(d) $\frac{28}{5}$ = $5\frac{3}{5}$
(e) $\frac{19}{6}$ = $3\frac{1}{6}$
(f) $\frac{35}{9}$ = $3\frac{8}{9}$

Q.3 Express the following as improper fractions:
(a) $7\frac{3}{4}$
(b) $5\frac{6}{7}$
(c) $2\frac{5}{6}$
(d) $10\frac{3}{5}$
(e) $9\frac{3}{7}$
(f) $8\frac{4}{9}$

Answer :

(a) $\frac{(7\times 4+3)}{4}=\frac{31}{4}$

$?$ The improper form is $\frac{31}{4}$
(b) $\frac{(5\times 7+6)}{7}=\frac{41}{7}$

$?$ The improper form is $\frac{41}{7}$
(c) $\frac{(2\times 6+5)}{6}=\frac{17}{6}$

$?$ The improper form is $\frac{17}{6}$
(d) $\frac{(10\times 5+3)}{5}=\frac{53}{5}$

$?$ The improper form is $\frac{53}{5}$
(e) $\frac{(9\times 7+3)}{7}=\frac{66}{7}$

$?$ The improper form is $\frac{66}{7}$
(f) $\frac{(8\times 9+4)}{9}=\frac{76}{9}$

$?$ The improper form is $\frac{76}{9}$

Q.1 Write the fractions. Are all these fractions equivalent?

Answer :

(a)
(i) The shaded portion is $\frac{1}{2}$
(ii) The shaded portion is$\frac{2}{4}=\frac{1}{2}$
(iii) The shaded portion is $\frac{3}{6}=\frac{1}{2}$
(iv) The shaded portion is $\frac{4}{8}=\frac{1}{2}$
Hence, all fractions are equivalent.
(b)
(i) The shaded portion is $\frac{4}{12}=\frac{1}{3}$
(ii) The shaded portion is$\frac{3}{9}=\frac{1}{3}$
(iii) The shaded portion is $\frac{2}{6}=\frac{1}{3}$
(iv) The shaded portion is $\frac{6}{15}=\frac{2}{5}$
Hence, all fractions are not equivalent.

Q.2 Write the fractions and pair up the equivalent fractions from each row.

Answer :

(a)$\frac{1}{2}$
(b) $\frac{4}{6}$ = $\frac{2}{3}$
(c) $\frac{3}{9}$ = $\frac{1}{3}$
(d) $\frac{2}{8}$ = $\frac{1}{4}$
(e) $\frac{3}{4}$
(i) $\frac{6}{18}$ = $\frac{1}{3}$
(ii) $\frac{4}{8}$ = $\frac{1}{2}$
(iii) $\frac{12}{16}$ = $\frac{3}{4}$
(iv) $\frac{8}{12}$ = $\frac{2}{3}$
(v) $\frac{4}{16}$ = $\frac{1}{4}$
The following are the equivalent fractions
(a) and (ii)
(b) and (iv)
(c) and (i)
(d) and (v)
(e) and (iii)

Q.3 Replace $?$in each of the following by the correct number:
(a) $\frac{2}{7}=\frac{8}{?}$
(b) $\frac{5}{8}=\frac{10}{?}$
(c) $\frac{3}{5}=\frac{?}{20}$
(d) $\frac{45}{60}=\frac{15}{?}$
(e) $\frac{18}{24}=\frac{?}{4}$

Answer :

(a) $\frac{2}{7}=\frac{8}{?}$
$?$ $\frac{2\times 4}{7\times 4}=\frac{8}{28}$
(b) $\frac{5}{8}=\frac{10}{?}$
$?$ $\frac{5\times 2}{8\times 2}=\frac{10}{16}$
(c) $\frac{3}{5}=\frac{?}{20}$
$?$ $\frac{3\times 4}{5\times 4}=\frac{12}{20}$
(d) $\frac{45}{60}=\frac{15}{?}$
$?$ $\frac{45÷3}{60÷3}=\frac{15}{20}$
(e) $\frac{18}{24}=\frac{?}{4}$
$?$ $\frac{18÷6}{24÷6}=\frac{3}{4}$

Q.4 Find the equivalent fraction of $\frac{3}{5}$having
(a) denominator 20
(b) numerator 9
(c) denominator 30
(d) numerator 27

Answer :

(a) We require denominator 20
Let M be the numerator of the fractions
$?\frac{M}{20}=\text{(}\frac{3}{5}$
5 × M = 20 × 3
M = (20 × 3) ÷ 5 = 12
Therefore the required fraction is $\frac{12}{20}$
(b) We require numerator 9
Let N be the denominator of the fractions
$?\frac{9}{N}=\text{(}\frac{3}{5}$
3 × N = 9 × 5
N = (9 × 5) ÷ 3 = 15
Therefore the required fraction is $\frac{9}{15}$
(c) We require denominator 30
Let D be the numerator of the fraction
$?\frac{D}{30}=\text{(}\frac{3}{5}$
5 × D = 3 × 30
D = (3 × 30) ÷ 5
= 18
Therefore the required fraction is $\frac{18}{30}$
(d) We require numerator 27
Let X be the denominator of the fraction
$?\frac{27}{X}=\text{(}\frac{3}{5}$
3 × X = 5 × 27
X = (5 × 27) ÷ 3 = 45
Therefore the required fraction is $\frac{27}{45}$

Q.5 Find the equivalent fraction of 36 / 48 with
(a) numerator 9
(b) denominator 4

Answer :

(a) Given numerator = 9
$?\frac{9}{X}=\frac{36}{48}$

X × 36 = 9 × 48
X = (9 × 48) / 36
X = 12
Hence, the equivalent fraction is $\frac{9}{12}$
(b) Given, denominator = 4
$?\frac{X}{4}=\frac{36}{48}$

X × 48 = 4 × 36
X = (4 × 36) / 48 = 3
Hence, the equivalent fraction is $\frac{3}{4}$

Q.6 Check whether the given fractions are equivalent:
(a) $\frac{5}{9},\frac{30}{54}$
(b) $\frac{3}{10},\frac{12}{50}$
(c) $\frac{7}{13},\frac{5}{11}$

Answer :

(a) Given $\frac{5}{9}$ and $\frac{30}{54}$
We have 5× 54 = 270
9 × 30 = 270
5 × 54 = 9 × 30
Hence, $\frac{5}{9}$ and $\frac{30}{54}$ are equivalent fractions
(b) Given $\frac{3}{10}$ and $\frac{12}{50}$
We have 3 × 50 = 150
10 × 12 = 120
3 × 50 $?$10 × 12
Hence, $\frac{3}{10}$ and $\frac{12}{50}$ are not equivalent fractions
(c) Given $\frac{7}{13}$ and $\frac{5}{11}$

We have 7 × 11 = 77
5 × 13 = 65
7 × 11 $?$ 5 × 13
Hence, $\frac{7}{13}$ and $\frac{5}{11}$ are not equivalent fractions

Q.7 Reduce the following fractions to simplest form:
(a) $\frac{48}{60}$
(b) $\frac{150}{60}$
(c) $\frac{84}{98}$
(d) $\frac{12}{52}$
(e) $\frac{7}{28}$

Answer :

(a) $\frac{48}{60}$ = $\frac{48÷12}{60÷12}$
= $\frac{4}{5}$
(b) $\frac{150}{60}$ = $\frac{150÷30}{60÷30}$
= $\frac{5}{2}$
(c) $\frac{84}{98}$= $\frac{84÷14}{98÷14}$
= $\frac{6}{7}$
(d) $\frac{12}{52}$ = $\frac{12÷4}{52÷4}$
= $\frac{3}{13}$
(e) $\frac{7}{28}$ = $\frac{7÷7}{28÷7}$
= $\frac{1}{4}$

Q.8 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Answer :

Total number of pencils Ramesh had = 20
Number of pencils used by Ramesh = 10